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Solve the following equation: ^4 , x , + , ^4 , x , = , , x

Question

Solve the following equation:
$sin^{4} x + cos^{4} x = sin x cos x .$

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Chloe Discussed

Solve the following equation:

sin^{4} x + cos^{4} x = sin x cos x .

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12 mins ago

Text solutionVerified

(sin^{2} x + cos^{2} x)^{2} - 2 sin^{2} x cos^{2} x = sin x cos x

Let

sin x cos x = z .

1 - 2 z^{2} = z

2 z^{2} + z - 1 = 0

2 z^{2} + 2 z - z - 1 = 0

(z + 1) (2 z - 1) = 0

So,

z = - 1, sin x cos x = - 1, sin 2 x = - 2. [Thus no value possible.]

2 z - 1 = 0, sin 2 x = 1, 2 x = 2 nπ + \frac{π}{2}, x = nπ + \frac{π}{4} .

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Question Text	Solve the following equation: $sin^{4} x + cos^{4} x = sin x cos x .$
Answer Type	Text solution:1
Upvotes	150